How can we numerically calculate integration like this in the picture, in which the denominator of the function becomes zero? any help will be appreciated.
This kind of integral usually appears in graphene and semi-metals. The denominator becomes zero at several points in the range of calculation, where Ω=2*ε.
Dudley J Benton
One way is to use Gauss quadrature, as it doesn't include the end points with the singularity. A high order should do it. I have the coefficients up to order 4096 free on my website. Another way is to transform the coordinates so that the singularity occurs at infinity. Then you can integrate out until the terms become insignificant.
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